775 lines
2.1 MiB
Plaintext
775 lines
2.1 MiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Regresja wielomianowa"
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]
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},
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{
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"source": [
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"\n",
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"\n",
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"Celem regresji wielomianowej jest zamodelowanie relacji między zmienną zależną od zmiennych niezależnych jako funkcję wielomianu n-tego stopnia.\n",
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"\n",
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"Postać ogólna regresji wielomianowej:\n",
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"\n",
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"$$ h_{\\theta}(x) = \\sum_{i=0}^{n} \\theta_i x^i $$\n",
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"\n",
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"Gdzie:\n",
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"\n",
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"$$ \\theta - \\text{wektor parametrów modelu} $$ "
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"source": [
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"## Funkcja kosztu\n",
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"\n",
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"\n",
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"W celu odpowiedniego dobrania parametrów modelu, trzeba znaleźć minimum funkcji kosztu zdefiniowanej poniższym wzorem:\n",
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"\n",
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"$$ J = \\frac{1}{2m} (X \\theta - y)^T (X \\theta - y) $$\n",
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"\n",
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"Gdzie:\n",
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"\n",
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"$$ m - \\text{ilość przykładów} $$ \n",
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"\n",
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"Za funkcję kosztu przyjmuje się zmodyfikowaną wersję błędu średniokwadratowego. Dodatkowo dodaje się dzielenie przez 2*m zamiast m, aby gradient z funkcji był lepszej postaci."
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"source": [
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"## Metoda gradientu prostego\n",
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""
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"source": [
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"Do znalezienia minimum funckji kosztu można użyć metody gradientu prostego. W tym celu iteracyjnie liczy się gradient funkcji kosztu i aktualizuje się za jego pomocą wektor parametrów modelu aż do uzyskania zbieżności (Różnica między obliczoną funkcją kosztu a funkcją kosztu w poprzedniej iteracji będzie mniejsza od ustalonej wcześniej wartości $\\varepsilon$).\n",
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"\n",
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"Gradient funkcji kosztu:\n",
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"\n",
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"$$ \\dfrac{\\partial J(\\theta)}{\\partial \\theta} = \\frac{1}{m}X^T(X \\theta - y)$$\n",
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"\n",
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"Modyfikacja parametrów modelu:\n",
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"\n",
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"$$ \\theta_{new} = \\theta - \\alpha * \\dfrac{\\partial J(\\theta)}{\\partial \\theta}$$\n",
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"\n",
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"Gdzie:\n",
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"\n",
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"$$ \\alpha - \\text{współczynnik uczenia} $$"
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],
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"cell_type": "markdown",
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"metadata": {}
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},
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{
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"cell_type": "code",
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"execution_count": 46,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"import ipywidgets as widgets\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import pandas\n",
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"\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 47,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"# Przydatne funkcje\n",
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"cost_functions = dict()\n",
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"\n",
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"def cost(theta, X, y):\n",
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" \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n",
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" m = len(y)\n",
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" J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n",
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" return J.item()\n",
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"\n",
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"def gradient(theta, X, y):\n",
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" \"\"\"Wersja macierzowa gradientu funkcji kosztu\"\"\"\n",
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" return 1.0 / len(y) * (X.T * (X * theta - y)) \n",
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"\n",
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"def gradient_descent(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-7):\n",
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" \"\"\"Algorytm gradientu prostego\"\"\"\n",
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" current_cost = fJ(theta, X, y)\n",
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" logs = [[current_cost, theta]]\n",
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" while True:\n",
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" theta = theta - alpha * fdJ(theta, X, y)\n",
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" current_cost, prev_cost = fJ(theta, X, y), current_cost\n",
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" # print(current_cost)\n",
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" if abs(prev_cost - current_cost) > 10**15:\n",
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" print('Algorytm nie jest zbieżny!')\n",
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" break\n",
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" if abs(prev_cost - current_cost) <= eps:\n",
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" break\n",
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" logs.append([current_cost, theta]) \n",
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" return theta, logs\n",
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"\n",
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"def plot_data(X, y, xlabel, ylabel):\n",
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" \"\"\"Wykres danych\"\"\"\n",
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" fig = plt.figure(figsize=(16*.6, 9*.6))\n",
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" ax = fig.add_subplot(111)\n",
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" fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
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" ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n",
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" \n",
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" ax.set_xlabel(xlabel)\n",
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" ax.set_ylabel(ylabel)\n",
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" ax.margins(.05, .05)\n",
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" plt.ylim(y.min() - 1, y.max() + 1)\n",
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" plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n",
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" return fig\n",
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"\n",
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"def plot_data_cost(X, y, xlabel, ylabel):\n",
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" \"\"\"Wykres funkcji kosztu\"\"\"\n",
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" fig = plt.figure(figsize=(16 * .6, 9 * .6))\n",
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" ax = fig.add_subplot(111)\n",
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" fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
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" ax.scatter([X], [y], c='r', s=50, label='Dane')\n",
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"\n",
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" ax.set_xlabel(xlabel)\n",
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" ax.set_ylabel(ylabel)\n",
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" ax.margins(.05, .05)\n",
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" plt.ylim(min(y) - 1, max(y) + 1)\n",
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" plt.xlim(np.min(X) - 1, np.max(X) + 1)\n",
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" return fig\n",
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"\n",
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"def plot_fun(fig, fun, X):\n",
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" \"\"\"Wykres funkcji `fun`\"\"\"\n",
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" ax = fig.axes[0]\n",
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" x0 = np.min(X[:, 1]) - 1.0\n",
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" x1 = np.max(X[:, 1]) + 1.0\n",
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" Arg = np.arange(x0, x1, 0.1)\n",
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" Val = fun(Arg)\n",
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" return ax.plot(Arg, Val, linewidth='2')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"metadata": {},
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"outputs": [],
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"source": [
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"def MSE(Y_true, Y_pred):\n",
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" \"\"\"Błąd średniokwadratowy - Mean Squared Error\"\"\"\n",
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" return np.square(np.subtract(Y_true,Y_pred)).mean()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"# Funkcja regresji wielomianowej\n",
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"\n",
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"def h_poly(Theta, x):\n",
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" \"\"\"Funkcja wielomianowa\"\"\"\n",
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" return sum(theta * np.power(x, i) for i, theta in enumerate(Theta.tolist()))\n",
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"\n",
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"def get_poly_data(data, deg):\n",
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" \"\"\"Przygotowanie danych do regresji wielomianowej\"\"\"\n",
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" m, n_plus_1 = data.shape\n",
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" n = n_plus_1 - 1\n",
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"\n",
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" X1 = data[:, 0:n]\n",
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" X1 /= np.amax(X1, axis=0)\n",
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"\n",
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" Xs = [np.ones((m, 1)), X1]\n",
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"\n",
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" for i in range(2, deg+1):\n",
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" Xn = np.power(X1, i)\n",
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" Xn /= np.amax(Xn, axis=0)\n",
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" Xs.append(Xn)\n",
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"\n",
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" X = np.matrix(np.concatenate(Xs, axis=1)).reshape(m, deg * n + 1)\n",
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"\n",
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" y = np.matrix(data[:, -1]).reshape(m, 1)\n",
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"\n",
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" return X, y\n",
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"\n",
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"\n",
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"def polynomial_regression(X, y, n):\n",
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" \"\"\"Funkcja regresji wielomianowej\"\"\"\n",
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" theta_start = np.matrix([0] * (n+1)).reshape(n+1, 1)\n",
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" theta, logs = gradient_descent(cost, gradient, theta_start, X, y)\n",
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" return lambda x: h_poly(theta, x), logs"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"metadata": {},
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"outputs": [],
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"source": [
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"def predict_values(model, data, n):\n",
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" \"\"\"Funkcja predykcji\"\"\"\n",
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" x, y = get_poly_data(np.array(data), n)\n",
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" preprocessed_x = []\n",
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" for i in x:\n",
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" preprocessed_x.append(i.item(1))\n",
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" return y, model(preprocessed_x), MSE(y, model(preprocessed_x))\n",
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"\n",
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"def plot_and_mse(data, data_test, n):\n",
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" \"\"\"Wykres wraz z MSE\"\"\"\n",
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" x, y = get_poly_data(np.array(data), n)\n",
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" model, logs = polynomial_regression(x, y, n)\n",
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" cost_function = [[element[0], i] for i, element in enumerate(logs)]\n",
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" cost_functions[n] = cost_function\n",
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" \n",
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" fig = plot_data(x, y, xlabel='x', ylabel='y')\n",
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" plot_fun(fig, model, x)\n",
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"\n",
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" y_true, Y_pred, mse = predict_values(model, data_test, n)\n",
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" print(f'Wielomian {n} stopnia, MSE = {mse}')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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" sqrMetres price\n",
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"1102 73 550000.0\n",
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"1375 78 496573.0\n",
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"1644 40 310000.0\n",
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"1434 22 377652.0\n",
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"1444 30 345180.0\n",
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"... ... ...\n",
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"384 76 269984.0\n",
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"214 42 249000.0\n",
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"24 47 299000.0\n",
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"1004 57 293848.0\n",
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"1632 112 329000.0\n",
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"\n",
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"[1674 rows x 2 columns]"
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],
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"text/html": "<div>\n<style scoped>\n .dataframe tbody tr th:only-of-type {\n vertical-align: middle;\n }\n\n .dataframe tbody tr th {\n vertical-align: top;\n }\n\n .dataframe thead th {\n text-align: right;\n }\n</style>\n<table border=\"1\" class=\"dataframe\">\n <thead>\n <tr style=\"text-align: right;\">\n <th></th>\n <th>sqrMetres</th>\n <th>price</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>1102</th>\n <td>73</td>\n <td>550000.0</td>\n </tr>\n <tr>\n <th>1375</th>\n <td>78</td>\n <td>496573.0</td>\n </tr>\n <tr>\n <th>1644</th>\n <td>40</td>\n <td>310000.0</td>\n </tr>\n <tr>\n <th>1434</th>\n <td>22</td>\n <td>377652.0</td>\n </tr>\n <tr>\n <th>1444</th>\n <td>30</td>\n <td>345180.0</td>\n </tr>\n <tr>\n <th>...</th>\n <td>...</td>\n <td>...</td>\n </tr>\n <tr>\n <th>384</th>\n <td>76</td>\n <td>269984.0</td>\n </tr>\n <tr>\n <th>214</th>\n <td>42</td>\n <td>249000.0</td>\n </tr>\n <tr>\n <th>24</th>\n <td>47</td>\n <td>299000.0</td>\n </tr>\n <tr>\n <th>1004</th>\n <td>57</td>\n <td>293848.0</td>\n </tr>\n <tr>\n <th>1632</th>\n <td>112</td>\n <td>329000.0</td>\n </tr>\n </tbody>\n</table>\n<p>1674 rows × 2 columns</p>\n</div>"
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},
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"metadata": {},
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"execution_count": 51
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}
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],
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"source": [
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"# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n",
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"\n",
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"alldata = pandas.read_csv('data_flats.tsv', header=0, sep='\\t',\n",
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" usecols=['price', 'rooms', 'sqrMetres'])\n",
|
|||
|
|
"alldata = alldata[['sqrMetres', 'price']]\n",
|
|||
|
|
"alldata = alldata.sample(frac=1)\n",
|
|||
|
|
"alldata"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 52,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"# alldata = np.matrix(alldata[['sqrMetres', 'price']])\n",
|
|||
|
|
"data_train = alldata[0:1600]\n",
|
|||
|
|
"data_test = alldata[1600:]\n",
|
|||
|
|
"data_train = np.matrix(data_train).astype(float)\n",
|
|||
|
|
"data_test = np.matrix(data_test).astype(float)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 53,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"name": "stdout",
|
|||
|
|
"text": [
|
|||
|
|
"Wielomian 1 stopnia, MSE = 49522013685.367744\n",
|
|||
|
|
"Wielomian 2 stopnia, MSE = 148367826800.28735\n",
|
|||
|
|
"Wielomian 3 stopnia, MSE = 145689760074.80402\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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|
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|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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|||
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|
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"source": [
|
|||
|
|
"cost_fun_slices = []\n",
|
|||
|
|
"for n in range(1, 4):\n",
|
|||
|
|
" plot_and_mse(data_train, data_test, n)\n",
|
|||
|
|
" \n",
|
|||
|
|
" cost_data = cost_functions.get(n)\n",
|
|||
|
|
" cost_x = [line[1] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_y = [line[0] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_fun_slices.append((cost_x, cost_y))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 54,
|
|||
|
|
"metadata": {},
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|||
|
|
"outputs": [
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|||
|
|
{
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|
|
"output_type": "display_data",
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"data": {
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},
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}
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},
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{
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"output_type": "display_data",
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"data": {
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|
|
"#WYKRESY FUNKCJI KOSZTU\n",
|
|||
|
|
"for fig in cost_fun_slices:\n",
|
|||
|
|
" cost_x, cost_y = fig\n",
|
|||
|
|
" fig = plot_data_cost(cost_x, cost_y, \"Iteration\", \"Cost function value\")"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 55,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"# Ilość nauki do oceny"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 56,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "execute_result",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
" number_courses time_study Marks\n",
|
|||
|
|
"0 3 4.508 19.202\n",
|
|||
|
|
"1 4 0.096 7.734\n",
|
|||
|
|
"2 4 3.133 13.811\n",
|
|||
|
|
"3 6 7.909 53.018\n",
|
|||
|
|
"4 8 7.811 55.299\n",
|
|||
|
|
".. ... ... ...\n",
|
|||
|
|
"95 6 3.561 19.128\n",
|
|||
|
|
"96 3 0.301 5.609\n",
|
|||
|
|
"97 4 7.163 41.444\n",
|
|||
|
|
"98 7 0.309 12.027\n",
|
|||
|
|
"99 3 6.335 32.357\n",
|
|||
|
|
"\n",
|
|||
|
|
"[100 rows x 3 columns]"
|
|||
|
|
],
|
|||
|
|
"text/html": "<div>\n<style scoped>\n .dataframe tbody tr th:only-of-type {\n vertical-align: middle;\n }\n\n .dataframe tbody tr th {\n vertical-align: top;\n }\n\n .dataframe thead th {\n text-align: right;\n }\n</style>\n<table border=\"1\" class=\"dataframe\">\n <thead>\n <tr style=\"text-align: right;\">\n <th></th>\n <th>number_courses</th>\n <th>time_study</th>\n <th>Marks</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>0</th>\n <td>3</td>\n <td>4.508</td>\n <td>19.202</td>\n </tr>\n <tr>\n <th>1</th>\n <td>4</td>\n <td>0.096</td>\n <td>7.734</td>\n </tr>\n <tr>\n <th>2</th>\n <td>4</td>\n <td>3.133</td>\n <td>13.811</td>\n </tr>\n <tr>\n <th>3</th>\n <td>6</td>\n <td>7.909</td>\n <td>53.018</td>\n </tr>\n <tr>\n <th>4</th>\n <td>8</td>\n <td>7.811</td>\n <td>55.299</td>\n </tr>\n <tr>\n <th>...</th>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n </tr>\n <tr>\n <th>95</th>\n <td>6</td>\n <td>3.561</td>\n <td>19.128</td>\n </tr>\n <tr>\n <th>96</th>\n <td>3</td>\n <td>0.301</td>\n <td>5.609</td>\n </tr>\n <tr>\n <th>97</th>\n <td>4</td>\n <td>7.163</td>\n <td>41.444</td>\n </tr>\n <tr>\n <th>98</th>\n <td>7</td>\n <td>0.309</td>\n <td>12.027</td>\n </tr>\n <tr>\n <th>99</th>\n <td>3</td>\n <td>6.335</td>\n <td>32.357</td>\n </tr>\n </tbody>\n</table>\n<p>100 rows × 3 columns</p>\n</div>"
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"execution_count": 56
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"data_marks_all = pandas.read_csv('Student_Marks.csv')\n",
|
|||
|
|
"data_marks_all"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 57,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"data_marks_all = data_marks_all[['time_study', 'Marks']]\n",
|
|||
|
|
"# data_marks_all = data_marks_all.sample(frac=1)\n",
|
|||
|
|
"data_marks_train = data_marks_all[0:70]\n",
|
|||
|
|
"data_marks_test = data_marks_all[70:]\n",
|
|||
|
|
"data_marks_train = np.matrix(data_marks_train).astype(float)\n",
|
|||
|
|
"data_marks_test = np.matrix(data_marks_test).astype(float)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 58,
|
|||
|
|
"metadata": {
|
|||
|
|
"tags": []
|
|||
|
|
},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"name": "stdout",
|
|||
|
|
"text": [
|
|||
|
|
"Wielomian 1 stopnia, MSE = 381.1693728350544\n",
|
|||
|
|
"Wielomian 2 stopnia, MSE = 394.1863119057109\n",
|
|||
|
|
"Wielomian 3 stopnia, MSE = 391.50171107305584\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
|
|||
|
|
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|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
}
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|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
|
|||
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|
|
},
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|
|
"metadata": {
|
|||
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|
"needs_background": "light"
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"cost_fun_slices = []\n",
|
|||
|
|
"\n",
|
|||
|
|
"for n in range(1, 4):\n",
|
|||
|
|
" plot_and_mse(data_marks_train, data_marks_test, n)\n",
|
|||
|
|
" \n",
|
|||
|
|
" cost_data = cost_functions.get(n)\n",
|
|||
|
|
" cost_x = [line[1] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_y = [line[0] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_fun_slices.append((cost_x, cost_y))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 59,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
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"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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{
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{
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|
|||
|
|
},
|
|||
|
|
"metadata": {
|
|||
|
|
"needs_background": "light"
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"#WYKRESY FUNKCJI KOSZTU\n",
|
|||
|
|
"for fig in cost_fun_slices:\n",
|
|||
|
|
" cost_x, cost_y = fig\n",
|
|||
|
|
" fig = plot_data_cost(cost_x, cost_y, \"Iteration\", \"Cost function value\")"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 60,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "execute_result",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": [
|
|||
|
|
" age sex bmi children smoker region charges\n",
|
|||
|
|
"319 32 male 37.335 1 no northeast 4667.60765\n",
|
|||
|
|
"832 28 female 23.845 2 no northwest 4719.73655\n",
|
|||
|
|
"79 41 female 32.965 0 no northwest 6571.02435\n",
|
|||
|
|
"74 44 male 27.400 2 no southwest 7726.85400\n",
|
|||
|
|
"603 64 female 39.050 3 no southeast 16085.12750\n",
|
|||
|
|
".. ... ... ... ... ... ... ...\n",
|
|||
|
|
"328 64 female 33.800 1 yes southwest 47928.03000\n",
|
|||
|
|
"447 56 female 25.650 0 no northwest 11454.02150\n",
|
|||
|
|
"320 34 male 25.270 1 no northwest 4894.75330\n",
|
|||
|
|
"575 58 female 27.170 0 no northwest 12222.89830\n",
|
|||
|
|
"756 39 female 22.800 3 no northeast 7985.81500\n",
|
|||
|
|
"\n",
|
|||
|
|
"[1338 rows x 7 columns]"
|
|||
|
|
],
|
|||
|
|
"text/html": "<div>\n<style scoped>\n .dataframe tbody tr th:only-of-type {\n vertical-align: middle;\n }\n\n .dataframe tbody tr th {\n vertical-align: top;\n }\n\n .dataframe thead th {\n text-align: right;\n }\n</style>\n<table border=\"1\" class=\"dataframe\">\n <thead>\n <tr style=\"text-align: right;\">\n <th></th>\n <th>age</th>\n <th>sex</th>\n <th>bmi</th>\n <th>children</th>\n <th>smoker</th>\n <th>region</th>\n <th>charges</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>319</th>\n <td>32</td>\n <td>male</td>\n <td>37.335</td>\n <td>1</td>\n <td>no</td>\n <td>northeast</td>\n <td>4667.60765</td>\n </tr>\n <tr>\n <th>832</th>\n <td>28</td>\n <td>female</td>\n <td>23.845</td>\n <td>2</td>\n <td>no</td>\n <td>northwest</td>\n <td>4719.73655</td>\n </tr>\n <tr>\n <th>79</th>\n <td>41</td>\n <td>female</td>\n <td>32.965</td>\n <td>0</td>\n <td>no</td>\n <td>northwest</td>\n <td>6571.02435</td>\n </tr>\n <tr>\n <th>74</th>\n <td>44</td>\n <td>male</td>\n <td>27.400</td>\n <td>2</td>\n <td>no</td>\n <td>southwest</td>\n <td>7726.85400</td>\n </tr>\n <tr>\n <th>603</th>\n <td>64</td>\n <td>female</td>\n <td>39.050</td>\n <td>3</td>\n <td>no</td>\n <td>southeast</td>\n <td>16085.12750</td>\n </tr>\n <tr>\n <th>...</th>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n <td>...</td>\n </tr>\n <tr>\n <th>328</th>\n <td>64</td>\n <td>female</td>\n <td>33.800</td>\n <td>1</td>\n <td>yes</td>\n <td>southwest</td>\n <td>47928.03000</td>\n </tr>\n <tr>\n <th>447</th>\n <td>56</td>\n <td>female</td>\n <td>25.650</td>\n <td>0</td>\n <td>no</td>\n <td>northwest</td>\n <td>11454.02150</td>\n </tr>\n <tr>\n <th>320</th>\n <td>34</td>\n <td>male</td>\n <td>25.270</td>\n <td>1</td>\n <td>no</td>\n <td>northwest</td>\n <td>4894.75330</td>\n </tr>\n <tr>\n <th>575</th>\n <td>58</td>\n <td>female</td>\n <td>27.170</td>\n <td>0</td>\n <td>no</td>\n <td>northwest</td>\n <td>12222.89830</td>\n </tr>\n <tr>\n <th>756</th>\n <td>39</td>\n <td>female</td>\n <td>22.800</td>\n <td>3</td>\n <td>no</td>\n <td>northeast</td>\n <td>7985.81500</td>\n </tr>\n </tbody>\n</table>\n<p>1338 rows × 7 columns</p>\n</div>"
|
|||
|
|
},
|
|||
|
|
"metadata": {},
|
|||
|
|
"execution_count": 60
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"data_ins = pandas.read_csv('insurance.csv')\n",
|
|||
|
|
"data_ins = data_ins.sample(frac=1)\n",
|
|||
|
|
"data_ins"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 61,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"data_ins = data_ins[['age', 'charges']]\n",
|
|||
|
|
"data_ins_train = data_ins[0:1200]\n",
|
|||
|
|
"data_ins_test = data_ins[1200:]\n",
|
|||
|
|
"data_ins_train = np.matrix(data_ins_train).astype(float)\n",
|
|||
|
|
"data_ins_test = np.matrix(data_ins_test).astype(float)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 62,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"output_type": "stream",
|
|||
|
|
"name": "stdout",
|
|||
|
|
"text": [
|
|||
|
|
"Wielomian 1 stopnia, MSE = 164742254.38173005\n",
|
|||
|
|
"Wielomian 2 stopnia, MSE = 165462756.34970585\n",
|
|||
|
|
"Wielomian 3 stopnia, MSE = 165419346.88711548\n"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"output_type": "display_data",
|
|||
|
|
"data": {
|
|||
|
|
"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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|
|
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},
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"metadata": {
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"needs_background": "light"
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|
}
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|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"cost_fun_slices = []\n",
|
|||
|
|
"\n",
|
|||
|
|
"for n in range(1, 4):\n",
|
|||
|
|
" plot_and_mse(data_ins_train, data_ins_test, n)\n",
|
|||
|
|
" \n",
|
|||
|
|
" cost_data = cost_functions.get(n)\n",
|
|||
|
|
" cost_x = [line[1] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_y = [line[0] for line in cost_data[:250]]\n",
|
|||
|
|
" cost_fun_slices.append((cost_x, cost_y))"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 63,
|
|||
|
|
"metadata": {},
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|||
|
|
"outputs": [
|
|||
|
|
{
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|
|
"output_type": "display_data",
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"data": {
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"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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},
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"metadata": {
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"needs_background": "light"
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}
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|
}
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|
],
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|||
|
|
"source": [
|
|||
|
|
"#WYKRESY FUNKCJI KOSZTU\n",
|
|||
|
|
"for fig in cost_fun_slices:\n",
|
|||
|
|
" cost_x, cost_y = fig\n",
|
|||
|
|
" fig = plot_data_cost(cost_x, cost_y, \"Iteration\", \"Cost function value\")"
|
|||
|
|
]
|
|||
|
|
}
|
|||
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|
],
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"metadata": {
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"author": "Paweł Skórzewski",
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"celltoolbar": "Slideshow",
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"email": "pawel.skorzewski@amu.edu.pl",
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3.9.5 64-bit",
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"metadata": {
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"interpreter": {
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"hash": "ac59ebe37160ed0dfa835113d9b8498d9f09ceb179beaac4002f036b9467c963"
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|
}
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}
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|
},
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|
"lang": "pl",
|
|||
|
|
"language_info": {
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|||
|
|
"codemirror_mode": {
|
|||
|
|
"name": "ipython",
|
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|
"version": 3
|
|||
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|
},
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|
"file_extension": ".py",
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|
"mimetype": "text/x-python",
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|
"name": "python",
|
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"nbconvert_exporter": "python",
|
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|
"pygments_lexer": "ipython3",
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"version": "3.9.5-final"
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|
},
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|
"livereveal": {
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|
"start_slideshow_at": "selected",
|
|||
|
|
"theme": "white"
|
|||
|
|
},
|
|||
|
|
"subtitle": "5.Regresja wielomianowa. Problem nadmiernego dopasowania[wykład]",
|
|||
|
|
"title": "Uczenie maszynowe",
|
|||
|
|
"year": "2021"
|
|||
|
|
},
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|
"nbformat": 4,
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"nbformat_minor": 4
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}
|